One sixth of the smallest of three consecutive even integers is three less than than one tenth the sum of the other two even integers. Find the integers.

n/6=((n+2) + (n+4))/10 - 3
n/6=(2n+6)/10-3
n/6=n/5+3/5-3
3-3/5=n/5-n/6
12/5=n/30

n=6*12=72

They are:
{72, 74, 76}